The present invention relates to a beam resonator in which high order resonant beam modes are generated. Beam modes are so named because they are mathematically identical to the possible cross-sectional power levels of a laser beam, H. Kogelnik and T. Li, "Laser Beams and Resonators", Applied Optics, 5, 1550 - 1567 (October, 1966), or the so-called beam waveguide, G. Goubau and F. Schwering, "On the Guided Propagation of Electromagnetic Wave Beams" , IRE Trans. on Antennas and Propagation, AP-9, 248 - 256 (May, 1961). The use of a Fabry-Perot structure as a laser resonator, along with its analogous relationship to the beam waveguide for transmission of very short wavelength microwave power, has provided the impetus for developing the electromagnetic theory of its operation. Measurements at microwave frequencies have often been used to verify the theory and analyze the effect of different parameters for a Fabry-Perot resonator.
A Fabry-Perot resonator is basically two mirrors positioned on a common axis and displaced from each other by a distance d. In systems with "large aperture", i.e., when a radial extent of the mirrors is large enough to reflect all but a negligible portion of beam energy, diffraction is neglected and a wave analysis of the resonator is carried out as follows.
A component of electric field, u, satisfied the scalar wave equation EQU .gradient..sup.2 u + k.sup.2 u = 0 (Equation 1)
where k = 2.pi./.lambda. is the propagation constant. Since energy is traveling back and forth in a primarily axial direction solutions of the form EQU u = .psi. (r,.theta. ,z)e.sup.-.sup.jkz (cylindrical coordinates)
or (Equation 2) EQU u = .psi. (x,y,z )e.sup.-.sup.jkz (cartesian coordinates)
are substituted into Equation 1 where e.sup.-.sup.jkz is a plane wave in the z direction and .psi. represents the difference between the beam in the cavity and a plane wave.
In the laser and beam waveguide technologies, the goal is to suppress high order modes, since they have a greater spatial extent and hence greater loss. Although observation of modes as high as TEM.sub.07 have been reported in the laser literature, they are not usually welcome in laser or beam waveguide technology.
In my previously mentioned co-pending patent application entitled "Proximity Sensor", I utilize perturbation of a resonant beam mode as the sensing mechanism. The beam mode resonator is chosen to resonate in a mode whose geometry coincides with a desired shape of an energy curtain. The presence of an object is inferred from its perturbing effects on the resonance parameters of the cavity.
In my proximity sensor, it is precisely the greater spatial extent of higher order beam modes which is exploited. Preferred embodiments of my proximity sensor utilize high order beam modes which form a cylindrical annular energy curtain or form an essentially planar energy curtain.